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Two circles with radius 1 are externally tangent at B and have AB and BC as diameters. A tangent to the circle with diameter BC passes through A, and a tangent to the circle with diameter AB passes through C so that the tangent lines are parallel. Find the distance between the two tangent lines.

 

Thank you!

 Oct 4, 2020
 #1
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We can use coordinates.  The equations of the lines are y = 1/3*(x + 2) and y = 1/3*(x - 2), and the distance between these lines is 2*sqrt(10)/5.

 Oct 4, 2020
 #2
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Sorry, I should have made it clear in the question. I would like some specific steps so that I know how to do these problems in the future. Thank you!

Noori  Oct 4, 2020
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Hello Noori,

 

To solve this problem we need to draw a diagram. We know that the tangents will be perpendicular to the radii drawn from their points of tangency, I just proved that yesterday, so we can draw a diagram, assume A' and C' are the centers of the tangent circles. Also, A, B, and C are colinear. Try to find the smallest distance between these lines, and build on this diagram!

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Pangolin14  Oct 4, 2020
 #4
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Hi Pangolin14. Thank you! Did you try to attach an image? It says Not Available?

Noori  Oct 4, 2020

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